Imagine the following situation:
Once upon a time, you get asked to do something. You are already extremely busy. Your dolist is overflowing with overdue items tagged "important" and though you're in the process of improving your time management/productivity skills, you still have a tendency for things to go from "Important & Not Urgent" to "I Will Die/Lose The Roof Over My Head".
The conversation goes like this:
Someone Else (SE): Could you take a look at X when you have time?
You (Y): Well, I'm very overloaded with critical things. Is it OK if I take a while before I get around to it? Is it important?
SE: Sure. It's not really that critical. Please do the stuff for project A (where A = a big critical project that sprouted lots of the important tasks, etc.) first, for starters.
Y: [giant sigh of relief] :)
Y: [Add thing to dolist as "not important/not urgent" with a due date of end-of-next-week]
The next week ends and you haven't gotten around to it. But that's fine because it's not important and not urgent.
Things happen and you never get around to the "not important/not urgent" tasks for 1 month+.
More time passes...
SE: Why haven't you looked at X?! You knew that it had to be done by the end of [name of month 3 months from the original conversation]! [more bad things happen]
How do you prevent this situation from happening? Assume that SE is someone important but not so important that you drop everything to do his bidding (for example, substitute "co-worker" for SE and not "CEO").
Imagine that X is actually a project and not something to just take a look at. Maybe it's "type up the notes from a 1 month trip, cross reference the photos, e-mail copies of photos to the people in the photos, and so on" and just breaking X down into individual steps is a time-consuming endeavor of its own.